An American flag flies at half staff in honor of those killed in the December 14 shootings at the Sandy Hook elementary school is reflected in raindrops on the window of a car in the center of Newtown, Connecticut, December 21. A moment of silence was observed in Newtown Friday and across the US followed by the ringing of church bells for each of the victims of the shootings.

“The majority of the threats in the past have turned out to be kids who make some very poor decisions and fail to recognize that what they view as a prank or a hoax is very likely to lead to their expulsion and prosecution,” Mr. Trump says. “However, all threats have to be treated seriously. You also have a small group of individuals in society ... with mental-health [or other] issues who are predisposed to potentially be violent, and a high-profile incident like Sandy Hook ... could push them over the top to act on their plans.”

• At Council Rock High School South in Holland, Pa., student reports of a fellow student’s threatening statements led police to arrest a ninth-grader Thursday. Two 9-mm handguns were in plain sight in the boy’s bedroom, and he was taken into custody, police say. The school canceled classes Friday so police could search the building. The Council Rock district is headquartered in Newtown, Pa., though police say there’s no indication the student mentioned the Newtown, Conn., shootings.

• On Monday, police say they found a high-caliber rifle and notes about a possible attack when they arrested an 18-year-old suspected of a plot against fellow students at Bartlesville High School in Oklahoma. In addition, the whole district closed Wednesday until after the holiday break because of reports of people seeing a man with a gun near a school.

• Two other Oklahoma school districts canceled classes Friday because of threats and rumors of possible violence.

• In Michigan, dozens of schools closed Friday. Many were related to Mayan doomsday rumors, but some arrests have also been made for students making threats on Facebook or telling classmates they’d bring a gun to school.

• Rumors of a student planning to bring a gun to school and kill himself led to the closure of Mountain Crest High School in Hyrum, Utah, Friday.

With so much media attention in the wake of the Sandy Hook tragedy, “there’s also a state of hypervigilance,” says Ronald Stephens, executive director of the National School Safety Center in Westlake Village, Calif. “Parents and others who see things in the community – the assumption is this is a potential threat that needs to be investigated.”

That can avert real threats, as appears to have been the case this week in Oklahoma and Pennsylvania.

It can also lead to something that later turns out to be harmless.

Eastern Carolina University in Greenville, N.C., was locked down for several hours Wednesday when people reported seeing a man with an assault rifle on campus. It turned out to be a long black umbrella, according to WRAL.com. The university handled the situation appropriately, police said.

School officials always have to do a balancing act when it comes to safety. One week after Sandy Hook, school officials would rather have to explain overreaction than another tragedy, Mr. Stephens suggests.

What’s key is that they have threat-assessment teams in place. “Administrators need help to reflect and evaluate the veracity [of threats],” he says.

Once school leaders are confident they have taken the appropriate steps, they may very well decide that a verbal threat in and of itself is not enough to close down a school or cancel an important activity.

Bill Bond had to make a tough decision as a principal when there was an anonymous bomb threat against Heath High School in West Paducah, Ky., as graduation approached in 1998. Earlier in the school year, in December 1997, a student had shot eight schoolmates, killing three of them.

The sheriff wanted to cancel graduation, but since there was time to bring in bomb-sniffing dogs, search the school thoroughly, post armed law-enforcement agents, and search people’s bags as they came in, Bond decided not to cancel.

“I said, ‘We’re going to have graduation.’... There has to be a time when you do everything you can, but you go on.”